Abstract: The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then
established in noncompact $FC$-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures.

Key words: minimax inequality, FC-subspace, FC-parametric-quasiconvex mapping